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Acoustic Scattering and the Extended Korteweg– de Vries Hierarchy

✍ Scribed by R. Beals; D.H. Sattinger; J. Szmigielski

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
266 KB
Volume
140
Category
Article
ISSN
0001-8708

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✦ Synopsis

The acoustic scattering operator on the real line is mapped to a Schro dinger operator under the Liouville transformation. The potentials in the image are characterized precisely in terms of their scattering data, and the inverse transformation is obtained as a simple, linear quadrature. An existence theorem for the associated Harry Dym flows is proved, using the scattering method. The scattering problem associated with the Camassa Holm flows on the real line is solved explicitly for a special case, which is used to reduce a general class of such problems to scattering problems on finite intervals.

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